correlation with categorical variables and significance test

[Fuga Iwama]

Hi,

I am confused with how to gain the correlation table with the multiple categorical variables.

I have independent variables such as social class, age group, income level and highest educational qualification as well as dummy variables such as sex.

Could you help me gain correlations between these categorical and dummy variables?

Also, to test for significance for each variable, could you put the standard error in the correlation table as well?

Thanks in advance!

[Nick Cox]

For a measured variable and a binary categorical variable, Pearson and Spearman correlations are necessarily identical, as ranks on the binary variable are just linear rescalings of 0 and 1. Think of this way: the graph is identical; it's just a case of whether 0 and 1 or the mean ranks for 0 and 1 are shown on the categorical axis.

For a measured variable and a ordinal categorical variable, Spearman and Kendall correlations are possible. You need to make a case that Pearson correlations make sense, as that amounts to saying that your scale is interval as well as ordinal.

For a measured variable and a nominal categorical variable, you need to say what kind of correlation makes sense. I'd buy the square root of R-square from a regression on the nominal variable treated as a factor variable.

I am not a great fan of the idea that the measurement scale implies which statistics make sense, but here I think it is cogent.

It follows that there is no such precisely defined thing as "the" correlation table here. You have to think and decide what you want.

[Fuga Iwama]

Thank you so much for the help!

[Marcos Almeida]

Also, to test for significance for each variable, could you put the standard error in the correlation table as well?

Please beware that a significant p-value for a correlation test is not necessarily "something extraordinary". It is just telling us that the correlation is different from zero. Then, a nasty question may arise: so what?